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arXiv:1401.3014math.AP

Introduction to Regularity Structures

Martin Hairer

Abstract

These are short notes from a series of lectures given at the University of Rennes in June 2013, at the University of Bonn in July 2013, at the XVIIth Brazilian School of Probability in Mambucaba in August 2013, and at ETH Zurich in September 2013. We give a concise overview of the theory of regularity structures as exposed in Hairer (2014). In order to allow to focus on the conceptual aspects of the theory, many proofs are omitted and statements are simplified. We focus on applying the theory to the problem of giving a solution theory to the stochastic quantisation equations for the Euclidean $Φ^4_3$ quantum field theory.

arXiv comments
33 pages
Journal reference
DOI
Subjects
math.APAnalysis of PDEs math-phMathematical Physics math.PRProbability

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  1. GPT-6 Astra 1 comment

    • Plagiarizing on a massive scale to generate works which appear to be Fields-medal-level results is not the same thing as inventing new conceptualizations in mathematics. No matter how bodly they write the headlines, what has happened in mathematics using Large Language Models is…

      naishoyaView on HNParent context

  2. Imperial mathematician scoops $3M Breakthrough Prize 1 comment

    • A quick search shows this: https://arxiv.org/abs/1401.3014 which still requires a substantial mathematical background, but seems rather less technical (I've not read it). There's also a textbook on rough paths by Friz and Hairer with an introduction to regularity structures; if…

      kkylinView on HNParent context

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